The search of candidates for \(\Sigma _3\)  leads us quite naturally to consider classification schemes for three-dimensional manifolds. For such a classification schema we will look towards the eight model geometries described in William Thurston's geometrization
conjecture [1]},
proven by Grigori Perelman in the early 2000s [2]}, [3]}, [4]}. In particular, we will consider the effect of the large-scale anisotropy inherent in these model geometries on the evolution of the Universe and how it deforms objects in the night sky.
